Unformatted text preview: μ = 0). Derive 2log Λ. What is the relationship between 2log Λ and ( ¯ X − μ ) /σ ? (2) Suppose σ 2 is not known. We want to test the hypotheses in (1), what is 2log Λ? What is the relationship between 2log Λ and ( ¯ X − μ ) /s , where s 2 = ∑ n i =1 ( X i − ¯ X ) 2 / ( n − 1)? (3) Suppose X 1 ,...,X n are0.4326 1.6656 0.1253 0.2877 1.1465 1.1909 1.1892 0.0376 0.3273 0.1746 We want to test H : μ = 0 versus H 1 : μ n = 0. Compute 2log Λ and compute the pvalue. Problem 5. Let X 1 ,...,X n ∼ Exp( λ ). We want to test H : λ = 1 versus H 1 : λ n = 1. (1) Derive 2log Λ. (2) Suppose X 1 ,...,X n are 2.8492 1.0417 0.2068 4.6191 1.9741 1.5957 1.6158 0.5045 1.3013 1.6154 Compute 2log Λ and compute the pvalue....
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 Winter '11
 Wu
 Statistics, Likelihoodratio test, likelihood ratio test, Likelihood principle

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